Ex 7.1, 2 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (i) 243
We see that
243 = 3 × 3 × 3 × 3 × 3
Since 3 does not occur in triplets,
∴ 243 is not a perfect cube.
So, we multiply by 3 to make triplet
So, our number becomes
243 × 3 = 3 × 3 × 3 × 3 × 3 × 3
Now, it becomes a perfect cube.
So, we multiply 243 by 3 to make it a perfect cube
Ex 7.1, 2 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (ii) 256
We see that
256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Since 2 does not occur in triplets,
∴ 256 is not a perfect cube.
So, we multiply by 2 to make triplet
So, our number becomes
256 × 2 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Now, it becomes a perfect cube.
So, we multiply 256 by 2 to make it a perfect cube
Ex 7.1, 2 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (iii) 72
We see that
72 = 2 × 2 × 2 × 3 × 3
Since 3 does not occur in triplets,
∴ 72 is not a perfect cube.
So, we multiply by 3 to make triplet
So, our number becomes
72 × 3 = 2 × 2 × 2 × 3 × 3 × 3
Now, it becomes a perfect cube.
So, we multiply 72 by 3 to make it a perfect cube
Ex 7.1, 2 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (iv) 675
We see that
675 = 3 × 3 × 3 × 5 × 5
Since 5 does not occur in triplets,
∴ 675 is not a perfect cube.
So, we multiply by 5 to make triplet
So, our number becomes
675 × 5 = 3 × 3 × 3 × 5 × 5 × 5
Now, it becomes a perfect cube.
So, we multiply 675 by 5 to make it a perfect cube
Ex 7.1, 2 Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (v) 100
We see that
100 = 2 × 2 × 5 × 5
Since 2 & 5 does not occur in triplets,
∴ 100 is not a perfect cube.
So, we multiply by 2 × 5 to make triplet
So, our number becomes
100 × 2 × 5 = 2 × 2 × 5 × 5 × 2 × 5
= 2 × 2 × 2 × 5 × 5 × 5
Now, it becomes a perfect cube.
So, we multiply 100 by 2 × 5
i.e. 10 to make it a perfect cube

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.